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We show that this algorithm offers substantial speedups of cumulant updates compared with the current solutions. The proposed algorithm can be used for processing on-line high-frequency multivariate data and can find applications, e.g., in on-line signal filtering and classification of data streams. To present an application of this algorithm, we propose an estimator of non-Gaussianity of a data stream based on the norms of high order cumulant tensors. We show how to detect the transition from Gaussian distributed data to non-Gaussian ones in a data stream. In order to achieve high implementation efficiency of operations on super-symmetric tensors, such as cumulant tensors, we employ a block structure to store and calculate only one hyper-pyramid part of such tensors.<\/jats:p>","DOI":"10.2478\/amcs-2019-0015","type":"journal-article","created":{"date-parts":[[2019,4,1]],"date-time":"2019-04-01T17:30:51Z","timestamp":1554139851000},"page":"195-206","source":"Crossref","is-referenced-by-count":4,"title":["An algorithm for arbitrary\u2013order cumulant tensor calculation in a sliding window of data streams"],"prefix":"10.61822","volume":"29","author":[{"given":"Krzysztof","family":"Domino","sequence":"first","affiliation":[{"name":"Institute of Theoretical and Applied Informatics , Polish Academy of Sciences , Ba\u0142tycka 5, 44-100 Gliwice , Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Piotr","family":"Gawron","sequence":"additional","affiliation":[{"name":"Institute of Theoretical and Applied Informatics , Polish Academy of Sciences , Ba\u0142tycka 5, 44-100 Gliwice , Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"37438","published-online":{"date-parts":[[2019,3,29]]},"reference":[{"key":"2023050302350548632_j_amcs-2019-0015_ref_001_w2aab3b7c14b1b6b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"Arismendi Zambrano, J. and Kimura, H. 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